Question

For which numbers, N, is N * 3 greater than 3? In other words, for which numbers, N, is N * 3 > 3? Consider all kinds of numbers for N: fractions, decimals, and positive, and negative numbers. Investigate this question by trying a number of examples and by thinking about the meaning and rules of multiplication.

A. A positive N > 1
B. A negative N < -1
C. Any N other than 0
D. No N can satisfy the condition.

Answer 1

The answer to the question is that any number other than 0, whether it's positive or negative, will result in a product greater than 3 when multiplied by 3.

Step-by-step explanation:

We need to find the range of numbers N for which N * 3 is greater than 3. Let's consider the different cases:

1. A. A positive N > 1: If N is a positive number greater than 1, then N * 3 will definitely be greater than 3. For example, if N = 2, then 2 * 3 = 6, which is greater than 3.
2. B. A negative N < -1: If N is a negative number less than -1, then N * 3 will also be greater than 3. For example, if N = -2, then -2 * 3 = -6, which is greater than 3.
3. C. Any N other than 0: Any number other than 0, whether it's positive or negative, will have a product greater than 3 when multiplied by 3. This is because when two positive numbers multiply, the answer has a positive sign as per the rules of multiplication. Similarly, when two negative numbers multiply, the answer has a positive sign. And when a negative number is multiplied by a positive number, the answer has a negative sign, but the absolute value is greater than 3.
4. D. No N can satisfy the condition: The condition N * 3 > 3 will not hold true only if N is equal to 0. When 0 is multiplied by 3, the result is 0, which is not greater than 3.

Therefore, the answer is option C. Any N other than 0 will satisfy the condition N * 3 > 3.